She said: “Oxbridge remains the equivalent of a finishing school for the private school system, polishing, refining and accentuating the elitism and sense of superiority acquired in earlier schooling.”

The academic called for quotas for certain groups to counteract “the growing class and race inequalities that are pervasive across the higher education sector”.

Despite efforts to overcome this issue, 42.6 per cent of Oxford students and 37 per cent of Cambridge students went to private school.

Prof Diane also raised ethnicity as a problem and said: “What we need is more radical action in terms of admissions, drawing lessons from affirmative action policies.

“Only then can we counteract the growing class and race inequalities that are pervasive across the HE sector. It is time for change.”

Last year’s stats show a white breakdown of 86 per cent at Oxford and 82 per cent at Cambridge.

Both unis responded they work hard to encourage more applications from black and minority ethic backgrounds.

A Cambridge spokesman said: “Success rates are influenced by prior school attainment, our entry requirements and the combinations of subjects studied by applicants.

“Data shows that ethnic minority admissions to Cambridge reflect national trends once prior school attainment has been factored in.

“Our commitment to improving access to the University is longstanding and unwavering.”

An Oxford spokesperson added: “We reject in the strongest terms any allegations of institutional bias or discrimination.

“Such claims are unsubstantiated, and we are concerned that unfounded allegations could undermine our efforts to attract and admit black and minority ethnic students.”